Allometric Scaling Of Metabolic Rate Research Articles

Metabolic scaling as an emergent outcome of variation in metabolic rate.

The allometric scaling of metabolic rate and what drives it are major questions in biology with a long history. Since the metabolic rate at any level of biological organization is an emergent property of its lower-level constituents, it is an outcome of the intrinsic heterogeneity among these units and the interactions among them. However, the influence of lower-level heterogeneity on system-level metabolic rate is difficult to investigate, given the tightly integrated body plan of unitary organisms. In this context, social insects such as honeybees can serve as important model systems because unlike unitary organisms, these superorganisms can be taken apart and reassembled in different configurations to study metabolic rate and its various drivers at different levels of organization. This commentary discusses the background of such an approach and how combining it with artificial selection to generate heterogeneity in metabolic rate with an analytical framework to parse out the different mechanisms that contribute to the effects of heterogeneity can contribute to the various models of metabolic scaling. Finally, the absence of the typical allometric scaling relationship among different species of honeybees is discussed as an important prospect for deciphering the role of top-down ecological factors on metabolic scaling. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

Allometric scaling of metabolic rate and cardiorespiratory variables in aquatic and terrestrial mammals.

While basal metabolic rate (BMR) scales proportionally with body mass (Mb ), it remains unclear whether the relationship differs between mammals from aquatic and terrestrial habitats. We hypothesized that differences in BMR allometry would be reflected in similar differences in scaling of O2 delivery pathways through the cardiorespiratory system. We performed a comparative analysis of BMR across 63 mammalian species (20 aquatic, 43 terrestrial) with a Mb range from 10 kg to 5318 kg. Our results revealed elevated BMRs in small (>10 kg and <100 kg) aquatic mammals compared to small terrestrial mammals. The results demonstrated that minute ventilation, that is, tidal volume (VT )·breathing frequency (fR ), as well as cardiac output, that is, stroke volume·heart rate, do not differ between the two habitats. We found that the "aquatic breathing strategy", characterized by higher VT and lower fR resulting in a more effective gas exchange, and by elevated blood hemoglobin concentrations resulting in a higher volume of O2 for the same volume of blood, supported elevated metabolic requirements in aquatic mammals. The results from this study provide a possible explanation of how differences in gas exchange may serve energy demands in aquatic versus terrestrial mammals.

Plasticity and evolution shape the scaling of metabolism and excretion along a geothermal temperature gradient

Abstract Physiological rates are heavily dependent on temperature and body size. Most current predictions of organisms’ response to environmental warming are based on the assumption that key physiological rates such as metabolism and excretion scale independently with body size and temperature and will not evolve. However, temperature is a significant driver for phenotypic variability in the allometric scaling and thermal sensitivity of physiological rates within ectotherm species, suggesting that evolution may play a role in shaping these parameters. We common‐reared six populations of western mosquitofish that have recently established (~100 years ago) in geothermal springs along a broad thermal gradient (19–33°C) to determine whether these scaling parameters are affected by evolutionary and/or plastic responses to warming over ecological timescales. Each population was reared at four different temperatures (23, 26, 30 and 32°C). We measured routine metabolic and nitrogen excretion rates on mosquitofish across a wide body size range. We found evidence for plasticity, but not evolution, increasing the allometric scaling of metabolic rate with temperature. Plasticity in metabolism allometry reflected a decrease in thermal sensitivity at smaller body sizes. We found evidence for evolution of phenotypic plasticity on the allometry of excretion rate, reflecting evolutionary differences in how thermal sensitivity varies with body size across different populations. Evolutionary differences in excretion rate scaling did not influence the relationship between excretion and metabolism across rearing temperatures, suggesting that warming does not affect the balance between mosquitofish energy demands and nutrient recycling rates. Read the free Plain Language Summary for this article on the Journal blog.

Larval nutrition impacts survival to adulthood, body size and the allometric scaling of metabolic rate in adult honeybees.

Resting metabolic rate (RMR) is a fundamental physiological measure linked to numerous aspects of organismal function, including lifespan. Although dietary restriction in insects during larval growth/development affects adult RMR, the impact of the nutritional composition of larval diets (i.e. diet quality) on adult RMR has not been studied. Using in vitro rearing to control larval diet quality, we determined the effect of dietary protein and carbohydrate on honeybee survival to adulthood, time to eclosion, body mass/size and adult RMR. High carbohydrate larval diets increased survival to adulthood and time to eclosion compared with both low carbohydrate and high protein diets. Upon emergence, bees reared on the high protein diet were smaller and lighter than those reared on other diets, whilst those raised on the high carbohydrate diet varied more in body mass. Newly emerged adult bees reared on the high carbohydrate diet showed a significantly steeper increase in allometric scaling of RMR compared with those reared on other diets. This suggests that the nutritional composition of larval diets influences survival to adulthood, time to eclosion and the allometric scaling of RMR. Given that agricultural intensification and increasing urbanisation have led to a decrease in both forage availability and dietary diversity for bees, our results are critical to improving understanding of the impacts of poor developmental nutrition on bee growth/development and physiology.

Coevolution of body size and metabolic rate in vertebrates: a life-history perspective.

ABSTRACTDespite many decades of research, the allometric scaling of metabolic rates (MRs) remains poorly understood. Here, we argue that scaling exponents of these allometries do not themselves mirror one universal law of nature but instead statistically approximate the non‐linearity of the relationship between MR and body mass. This ‘statistical’ view must be replaced with the life‐history perspective that ‘allows’ organisms to evolve myriad different life strategies with distinct physiological features. We posit that the hypoallometric allometry of MRs (mass scaling with an exponent smaller than 1) is an indirect outcome of the selective pressure of ecological mortality on allocation ‘decisions’ that divide resources among growth, reproduction, and the basic metabolic costs of repair and maintenance reflected in the standard or basal metabolic rate (SMR or BMR), which are customarily subjected to allometric analyses. Those ‘decisions’ form a wealth of life‐history variation that can be defined based on the axis dictated by ecological mortality and the axis governed by the efficiency of energy use. We link this variation as well as hypoallometric scaling to the mechanistic determinants of MR, such as metabolically inert component proportions, internal organ relative size and activity, cell size and cell membrane composition, and muscle contributions to dramatic metabolic shifts between the resting and active states. The multitude of mechanisms determining MR leads us to conclude that the quest for a single‐cause explanation of the mass scaling of MRs is futile. We argue that an explanation based on the theory of life‐history evolution is the best way forward.

Metabolic rate scaling, ventilation patterns and respiratory water loss in red wood ants: activity drives ventilation changes, metabolic rate drives water loss.

Metabolic rate and its relationship with body size is a fundamental determinant of many life history traits and potentially of organismal fitness. Alongside various environmental and physiological factors, the metabolic rate of insects is linked to distinct ventilation patterns. Despite significant attention, however, the precise role of these ventilation patterns remains uncertain. Here, we determined the allometric scaling of metabolic rate and respiratory water loss in the red wood ant, as well as assessing the effect of movement upon metabolic rate and ventilation pattern. Metabolic rate and respiratory water loss are both negatively allometric. We observed both continuous and cyclic ventilation associated with relatively higher and lower metabolic rates, respectively. In wood ants, however, movement not metabolic rate is the primary determinant of which ventilation pattern is performed. Conversely, metabolic rate not ventilation pattern is the primary determinant of respiratory water loss. Our statistical models produced a range of relatively shallow intraspecific scaling exponents between 0.40 and 0.59, emphasising the dependency upon model structure. Previous investigations have revealed substantial variation in morphological allometry among wood ant workers from different nests within a population. Metabolic rate scaling does not exhibit the same variability, suggesting that these two forms of scaling respond to environmental factors in different ways.

Dental functional morphology predicts the scaling of chewing rate in mammals

How food intake and mastication scale to satisfy the metabolic needs of mammals has been the subject of considerable scientific debate. Existing theory suggests that the negative allometric scaling of metabolic rate with body mass is compensated by a matching allometric scaling of the chewing rate. Why empirical studies have found that the scaling coefficients of the chewing rate seem to be systematically smaller than expected from theory remains unknown. Here we explain this imparity by decoupling the functional surface area of teeth from overall surface area. The functional surface area is relatively reduced in forms emphasizing linear edges (e.g., lophodont) compared with forms lacking linear structures (e.g., bunodont). In forms with reduced relative functional surface, the deficit in food processed per chew appears to be compensated for by increased chewing rate, such that the metabolic requirements are met. This compensation accounts for the apparent difference between theoretically predicted and observed scaling of chewing rates. We suggest that this reflects adaptive functional evolution to plant foods with different fracture properties and extend the theory to incorporate differences in functional morphology.

Physiological, morphological, and ecological tradeoffs influence vertical habitat use of deep-diving toothed-whales in the Bahamas.

Dive capacity among toothed whales (suborder: Odontoceti) has been shown to generally increase with body mass in a relationship closely linked to the allometric scaling of metabolic rates. However, two odontocete species tagged in this study, the Blainville’s beaked whale Mesoplodon densirostris and the Cuvier’s beaked whale Ziphius cavirostris, confounded expectations of a simple allometric relationship, with exceptionally long (mean: 46.1 min & 65.4 min) and deep dives (mean: 1129 m & 1179 m), and comparatively small body masses (med.: 842.9 kg & 1556.7 kg). These two species also exhibited exceptionally long recovery periods between successive deep dives, or inter-deep-dive intervals (M. densirostris: med. 62 min; Z. cavirostris: med. 68 min). We examined competing hypotheses to explain observed patterns of vertical habitat use based on body mass, oxygen binding protein concentrations, and inter-deep-dive intervals in an assemblage of five sympatric toothed whales species in the Bahamas. Hypotheses were evaluated using dive data from satellite tags attached to the two beaked whales (M. densirostris, n = 12; Z. cavirostris, n = 7), as well as melon-headed whales Peponocephala electra (n = 13), short-finned pilot whales Globicephala macrorhynchus (n = 15), and sperm whales Physeter macrocephalus (n = 27). Body mass and myoglobin concentration together explained only 36% of the variance in maximum dive durations. The inclusion of inter-deep-dive intervals, substantially improved model fits (R2 = 0.92). This finding supported a hypothesis that beaked whales extend foraging dives by exceeding aerobic dive limits, with the extension of inter-deep-dive intervals corresponding to metabolism of accumulated lactic acid. This inference points to intriguing tradeoffs between body size, access to prey in different depth strata, and time allocation within dive cycles. These tradeoffs and resulting differences in habitat use have important implications for spatial distribution patterns, and relative vulnerabilities to anthropogenic impacts.

Mitochondrial Function and Cell Size: An Allometric Relationship.

Allometric scaling of metabolic rate results in lower total mitochondrial oxygen consumption with increasing organismal size. This is considered a universal law in biology. Here, we discuss how allometric laws impose size-dependent limits to mitochondrial activity at the cellular level. This cell-size-dependent mitochondrial metabolic activity results in nonlinear scaling of metabolism in proliferating cells, which can explain size homeostasis. The allometry in mitochondrial activity can be controlled through mitochondrial fusion and fission machinery, suggesting that mitochondrial connectivity can bypass transport limitations, the presumed biophysical basis for allometry. As physical size affects cellular functionality, cell-size-dependent metabolism becomes directly relevant for development, metabolic diseases, and aging.

Does the membrane pacemaker theory of metabolism explain the size dependence of metabolic rate in marine mussels?

According to the membrane pacemaker theory of metabolism (MPT), allometric scaling of metabolic rate in animals is determined by the composition of cellular and mitochondrial membranes, which changes with body size in a predictable manner. MPT has been elaborated from interspecific comparisons in mammals. It projects that the degree of unsaturation of membrane phospholipids decreases in larger organisms, thereby lowering ion permeability of the membranes and making cellular, and thus whole-animal metabolism more efficient. Here, we tested the applicability of the MPT to a marine ectotherm, the mussel Mytilus edulis at the intraspecific level. We determined effects of body mass on whole-organism, tissue and cellular oxygen consumption rates, on heart rate, metabolic enzyme activities and on the lipid composition of membranes. In line with allometric patterns, the organismal functions and processes such as heart rate, whole-animal respiration rate and phospholipid contents showed a mass-dependent decline. However, the allometry of tissue and cellular respiration and activity of metabolic enzymes was poor; fatty acid unsaturation of membrane phospholipids of gill tissue was independent of animal size. It is thus conceivable that most of the metabolic allometry observed at the organismal level is determined by systemic functions. These whole-organism patterns may be supported by energy savings associated with growing cell size but not by structural changes in membranes. Overall, the set of processes contributing to metabolic allometry in ectotherms may differ from that operative in mammals and birds, with a reduced involvement of the mechanisms proposed by the MPT.

Temperature effects on mass-scaling exponents in colonial animals: a manipulative test.

Body size and temperature are fundamental drivers of ecological processes because they determine metabolic rates at the individual level. Whether these drivers act independently on individual-level metabolic rates remains uncertain. Most studies of intraspecific scaling of unitary organisms must rely on preexisting differences in size to examine its relationship with metabolic rate, thereby potentially confounding size-correlated traits (e.g., age, nutrition) with size, which can affect metabolic rate. Here, we use a size manipulation approach to test whether metabolic mass scaling and temperature dependence interact in four species (two phyla) of colonial marine invertebrates. Size manipulation in colonial organisms allows tests of how ecological processes (e.g., predation) affect individual physiology and consequently population- and community-level energy flux. Body mass and temperature interacted in two species, with one species exhibiting decreased and the other increased mass-scaling exponents with increasing temperature. The allometric scaling of metabolic rate that we observe in three species contrasts with the isometric scaling of ingestion rates observed in some colonial marine invertebrates. Thus, we suggest that the often observed competitive superiority of colonial over unitary organisms may arise because the difference between energy intake and expenditure increases more strongly with size in colonial organisms.

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels.

Heterogeneity of cells may explain allometric scaling of metabolic rate

The origin of allometric scaling of metabolic rate is a long-standing question in biology. Several models have been proposed for explaining the origin; however, they have advantages and disadvantages. In particular, previous models only demonstrate either two important observations for the allometric scaling: the variability of scaling exponents and predominance of 3/4-power law. Thus, these models have a dispute over their validity. In this study, we propose a simple geometry model, and show that a hypothesis that total surface area of cells determines metabolic rate can reproduce these two observations by combining two concepts: the impact of cell sizes on metabolic rate and fractal-like (hierarchical) organization. The proposed model both theoretically and numerically demonstrates the approximately 3/4-power law although several different biological strategies are considered. The model validity is confirmed using empirical data. Furthermore, the model suggests the importance of heterogeneity of cell size for the emergence of the allometric scaling. The proposed model provides intuitive and unique insights into the origin of allometric scaling laws in biology, despite several limitations of the model.

When do evolutionary food web models generate complex networks?

Evolutionary foodweb models are used to build food webs by the repeated addition of new species. Population dynamics leads to the extinction or establishment of a newly added species, and possibly to the extinction of other species. The food web structure that emerges after some time is a highly nontrivial result of the evolutionary and dynamical rules. We investigate the evolutionary food web model introduced by Loeuille and Loreau (2005), which characterizes species by their body mass as the only evolving trait. Our goal is to find the reasons behind the model's remarkable robustness and its capability to generate various and stable networks. In contrast to other evolutionary food web models, this model requires neither adaptive foraging nor allometric scaling of metabolic rates with body mass in order to produce complex networks that do not eventually collapse to trivial structures. Our study shows that this is essentially due to the fact that the difference in niche value between predator and prey as well as the feeding range are constrained so that they remain within narrow limits under evolution. Furthermore, competition between similar species is sufficiently strong, so that a trophic level can accommodate several species. We discuss the implications of these findings and argue that the conditions that stabilize other evolutionary food web models have similar effects because they also prevent the occurrence of extreme specialists or extreme generalists that have in general a higher fitness than species with a moderate niche width.

Larger laboratory colonies consume proportionally less energy and have lower per capita brood production in Temnothorax ants

Colony size can affect individual- and colony-level behavioral and physiological traits in social insects. Changes in behavior and physiology in response to colony growth and development can affect productivity and fitness. Here, we used respirometry to study the relationship between colony size and colony energy consumption in Temnothorax rugatulus ants. In addition, we examined the relationship between colony size and worker productivity measured as per capita brood production. We found that colony metabolic rate scales with colony size to the 0.78 power and the number of brood scales with the number of workers to the 0.49 power. These regression analyses reveal that larger ant colonies use proportionally less energy and produce fewer brood per worker. Our findings provide new information on the relationships between colony size and energetic efficiency and productivity in a model ant genus. We discuss the potential mechanisms giving rise to allometric scaling of metabolic rate in ant colonies and the influence of colony size on energy consumption and productivity in general.

Metabolic principles of river basin organization

The metabolism of a river basin is defined as the set of processes through which the basin maintains its structure and responds to its environment. Green (or biotic) metabolism is measured via transpiration and blue (or abiotic) metabolism through runoff. A principle of equal metabolic rate per unit area throughout the basin structure is developed and tested in a river basin characterized by large heterogeneities in precipitation, vegetation, soil, and geomorphology. This principle is suggested to have profound implications for the spatial organization of river basin hydrologic dynamics, including the minimization of energy expenditure known to control the scale-invariant characteristics of river networks over several orders of magnitude. Empirically derived, remarkably constant rates of average transpiration per unit area through the basin structure lead to a power law for the probability distribution of transpiration from a randomly chosen subbasin. The average runoff per unit area, evaluated for subbasins of a wide range of topological magnitudes, is also shown to be remarkably constant independently of size. A similar result is found for the rainfall after accounting for canopy interception. Allometric scaling of metabolic rates with size, variously addressed in the biological literature and network theory under the label of Kleiber's law, is similarly derived. The empirical evidence suggests that river basin metabolic activity is linked with the spatial organization that takes place around the drainage network and therefore with the mechanisms responsible for the fractal geometry of the network, suggesting a new coevolutionary framework for biological, geomorphological, and hydrologic dynamics.

Allometric Scaling of Metabolism, Growth, and Activity in Whole Colonies of the Seed‐Harvester AntPogonomyrmex californicus

The negative allometric scaling of metabolic rate with body size is among the most striking patterns in biology. We investigated whether this pattern extends to physically independent eusocial systems by measuring the metabolic rates of whole functioning colonies of the seed-harvester ant Pogonomyrmex californicus. These intraspecific scaling data were compared to the predictions of an additive model developed to estimate collective metabolic rates. Contrary to the prediction of the additive model, colony metabolic rate allometry resembled the pattern commonly observed interspecifically for individual organisms, scaling with colony mass(0.75). Among the same-aged colonies, net growth rate varied by up to sevenfold, with larger colonies exhibiting higher net growth efficiency than smaller colonies. Isolated worker groups exhibited isometric metabolic rate scaling, suggesting that the social environment of the colony is critical to regulating individual patterns of work output. Within the social environment, individual worker locomotor velocities exhibited power-law distributions that scaled with colony size so that larger colonies exhibited a greater disparity between active and inactive ants than did smaller colonies. These results demonstrate that behavioral organization within colonies may have a major influence on colony-level metabolism and in generating intraspecific variation in growth trajectories.

Toward a General Theory for How Climate Change Will Affect Infectious Disease

Toward a General Theory for How Climate Change Will Affect Infectious Disease

Scaling of metabolic rate in the lesser wax mothAchroia griselladoes not fit the 3/4-power law and shows significant sex differences

Allometric scaling of metabolic rates is commonly described as a power function and 0.75 is a widely accepted exponent. The universality of this exponent is in doubt and, particularly for insects, contradictory results have been obtained. Furthermore, sexual differences in scaling exponents are observed for several species that could lead to artefacts when they are not considered in intra- and interspecific scaling. Whether the metabolic scaling exponent in the lesser wax moth Achroia grisella differs significantly from 0.75 is tested, as well as whether it differs between the sexes. Adults of this moth neither feed nor drink, rendering them as suitable subjects for a study of metabolic rates. Neglecting sex differences, a metabolic scaling exponent of 0.8 is recorded. However, there are significant differences in metabolic scaling between the sexes. When considered separately, males scale with 0.96 and females with 0.67. Thus, in this species, a scaling exponent of 0.75 does not appear to exist either for males or females. The body size optimization model offers a potential explanation for the sex differences in metabolic scaling, although it remains to be tested in wax moths. With insects in particular, there is the need for more detailed studies on the scaling of metabolic rates that also take sexual differences into account.

Quantum metabolism explains the allometric scaling of metabolic rates

A general model explaining the origin of allometric laws of physiology is proposed based on coupled energy-transducing oscillator networks embedded in a physical d-dimensional space (d = 1, 2, 3). This approach integrates Mitchell's theory of chemi-osmosis with the Debye model of the thermal properties of solids. We derive a scaling rule that relates the energy generated by redox reactions in cells, the dimensionality of the physical space and the mean cycle time. Two major regimes are found corresponding to classical and quantum behaviour. The classical behaviour leads to allometric isometry while the quantum regime leads to scaling laws relating metabolic rate and body size that cover a broad range of exponents that depend on dimensionality and specific parameter values. The regimes are consistent with a range of behaviours encountered in micelles, plants and animals and provide a conceptual framework for a theory of the metabolic function of living systems.